Fractions+Core+Concepts,Skills,Strategies

Fractions Concepts/SKills/Strategies

(Welcome to Miss. Klines 1st Grade Class!, n.d.)


 * = Description of the concept/skill/strategy ||= Teaching the concept/skill/strategy ||= Four stage language model ||
 * Concept: The part-whole relationship involves the recognition of the relationship between the part and the whole. Concrete materials are used to introduce the part-whole relationship. This concept allows children to visualise the relationship between the part and the whole and the meaning of the relative size of a part to a whole. Area models are useful models to demonstrate this concept. || Start with real life materials before moving onto other concrete materials, which will assist students understanding during the Student's language stage.

I have a whole cake. You can see that I have one whole round cake. I want to share the cake evenly with one of my friends.

I will need to cut the cake into 2 equal pieces, to share it equally with my friend. Lets cut the cake into 2 equal sized pieces.

We can see that I have 1 part out of 2 equal parts altogether. 1 part out of 2 equal parts for me and 1 part out of 2 equal parts for my friend. We can see that there are 2 equal sized pieces within the whole cake.

We can say that we each have one half of the whole cake.

2 equal sized pieces can be made from the whole. These equal pieces can form together to make a whole.

My friend and I each have an equal sized share of the cake. || Students Language Stage ||
 * Skill: The fraction algorithm is a skill used to solve fractional addition problems. The symbolic algorithm can be used in conjunction with area models, such as fraction circles or fraction pieces. When the algorithm is used with area models, it allows students to develop mental images of the sizes of different pieces. Area models, allow students to visualise the different sized pieces and move and manipulate the models to find the same sized pieces so the addition problem can be carried out. Students can carry out the fraction problem using models and write the symbolic language on the fraction algorithm. ||= I would begin with the symbolic algorithm 1 and one half add 1 and one quarter and set it out vertically like other algorithms.

We can see that we have 1 whole and 1 part out of 2 equal parts and 1 whole and 1 part out of 4 equal parts that we need to add together. We need to find how many wholes and fractional parts of the whole that there are altogether.

Let's use fractional pieces to help us demonstrate the written algorithm. Place the whole pieces under the whole section of the algorithm and the fractional parts of a whole under the fractional parts heading.

First, we will start on the left side of the algorithm and add the wholes together. We can see that we have 2 wholes (write down on symbolic algorithm).

Let's place one part out of two equal parts of the whole on the algorithm table, we can say that this is one half. Let's place one part out of four equal parts of the whole on the algorithm table, we can say that this is one quarter. So we need to add one half and one quarter. What is one half and one quarter? It is very difficult to add halves and quarters because they are different sized pieces. If we change the halves and the quarters into the same sized pieces we can add them both together easily. What can we change both halves and quarters into? We can change halves into quarters. So if I change my half into 2 quarters, and I know there the same because there are no gaps when I put them on top of each other. Now I can add them together. 2 quarters add 1 quarter is 3 quarters. So one half add one quarter is 3 quarters.

We can write it on our algorithm like this (picture below). One part out of two equal parts of the whole or one half is equivalent to two quarters. We needed to change the half to quarters to allow us to add the fractional pieces of the whole together easily. We have 2 wholes and 3 parts out of four equal parts of the whole. 1 and 1 half add 1 and 1 quarter is 2 and 3 quarters altogether. || Mathematics Language Stage Symbolic Language Stage ||
 * Strategy: Equivalent fractions are fractions that represent the same amount. Equivalent fractions may look different yet they have the same value. Using the concrete resource of fraction mats, students can visually manipulate the mats in comparison to the whole to work out equivalent fractions. Students can take a fraction and can use the fraction mats to work out the equivalent fraction by placing the equal parts of another fraction on top of the initial fraction. The fraction mats allow the student to visually recognise the equivalent fraction, and reiterates that even though the fraction may appear different, there value can still be equal. || I would begin by using fraction mats to demonstrate equivalent fractions to students, during the materials and mathematics language stage. This strategy could be commenced once the initial concept and skill had been developed.

I would begin by having 1 whole fraction piece in the center of an Overhead Transparency (OHT). I would use this whole fractional piece to relate the fractional part to the whole.

Here we have 2 equal parts, each one could be called one part out of 2 equal parts or one half.

Here we have 4 equal parts, each one could be called one part out of 4 equal parts or one quarter.

Here we have 6 equal parts, each one could be called one part out of 6 equal parts or one sixth.

Let's look at how many halves are the same as one quarter.

Put the quarters on top of the halves. We can see that two quarters is the same as one half.

Let's look at the sixths. Let's find out how many sixths are the same as one half. Three sixths is the same as one half. These are what we call equivalent fractions. We can use the fraction mats to help us identify the equivalent fraction of one half.

We have identified that even though the fractions look different they are equivalent.

We can say that two quarters and three sixths is equivalent to one half. || Materials Language Stage Mathematics Language Stage ||

Welcome to Miss. Kline's 1st Grade Class! (n.d.). Fractions [image]. Retrieved September 21, 2010 from http://polaris.umuc.edu/~skline/math.html